The problem is that you need an image that is easy to print and duplicate. The fancy ones with multicolors are going to be very difficult to print and put on stuff. In addition, a lot of those images look like they are meant for airbrushing and tattoos.
Based on my experiences in print media trying to get several company logos printed on documents and on stuff like pencils, baseball caps, t-shirts and other stuff, I would recommend something with a single color and simple outline. (In a past job a long time ago, I was responsible for working with printers to produce marketing materials and get our logo on stationery and giveaways.)
I found this more simple phoenix image:
http://www.canstockphoto.com/phoenix-color-14384034.html I like the pink version because it looks feminine and still looks like a phoenix. We would have to purchase rights to use it for multiple things, but that would just take a few of us to chip in initially.
Another image I am attracted to is a roseate spoonbill. They are a pink Florida bird. In searching for images, I found this single pink feather that I thought was interesting:
http://www.paulmarcellini.com/photo/roseate-spoonbill-feather/ This image is a photo, but we could find a clipart feather and color it.
How about the pink feather on the second row, far left?
http://angiemakes.com/free-feather-clip-art/ A pink feather could symbolize a phoenix or anything else we wanted it to symbolize and it would be unique. This one has sharp edges and is simple so it would print and copy well onto just about anything.
The neat thing about a single feather is that the meaning would be something meaningful to us but that no one else would know unless they came onto this forum. It is simple, but distinct, and I don't know any other group of any kind that uses a feather as a logo.